1. In a large bowl, combine the flour and salt. Cut in the chilled butter until the mixture resembles coarse crumbs. Gradually add the ice water, mixing just until the dough comes together. Divide the dough into two equal discs, wrap in plastic, and refrigerate for at least 30 minutes.

2. In a large skillet over medium-high heat, cook the ground beef, breaking it up as it cooks, until no longer pink, about 5-7 minutes. Drain any excess fat.

3. Add the onion, carrots, celery, and garlic to the skillet. Cook, stirring occasionally, until the vegetables are softened, about 8-10 minutes.

4. Stir in the thyme, rosemary, beef broth, and Worcestershire sauce. Season with salt and pepper to taste. Simmer for 15-20 minutes, until the sauce has thickened.

5. Preheat the oven to 400°F (200°C).

6. On a lightly floured surface, roll out one disc of dough to fit a 9-inch pie dish. Gently transfer the dough to the dish and press it into the bottom and up the sides.

7. Spoon the beef mixture into the prepared pie crust. Roll out the remaining dough to fit the top of the pie. Place the dough over the filling and crimp the edges to seal.

8. Cut a few slits in the top of the pie to allow steam to escape. Brush the top with the egg wash.

9. Bake for 30-35 minutes, until the crust is golden brown. Allow to cool for 10 minutes before serving.